Final answer:
The nurse should first auscultate the breath sounds to assess the patient's respiratory status.
Step-by-step explanation:
The nurse should first auscultate the breath sounds.
In this scenario, the patient with a history of chronic heart failure is presenting with severe dyspnea and a dry, hacking cough. Auscultating the breath sounds would be the most appropriate action to assess the patient's respiratory status. Crackling or abnormal sounds could indicate pulmonary congestion or fluid accumulation in the lungs, which may be related to the heart failure. This assessment would guide further interventions and treatment.